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A meeting point (Posted on 2018-01-07) Difficulty: 3 of 5
The lines with equations:
y = x + 1,
y = mx − 1,
& y = −4x + 2m
pass through the same point.

Determine all possible values for m.

See The Solution Submitted by Ady TZIDON    
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Solution Comment 2 of 2 |
This is really just a system of three equations in 3 unknowns.

Equate the first and second and solve for x:
x=2/(m-1)
Equate the first and third and solve for x:
x=(2m-1)/5

Equate these two and solve for m:
0=m^2 - 3m - 9
0=(2m+3)(m-3)
The solutions are
m=-3/2 or m=3

The corresponding intersection points are (-4/5,1/5) & (1,2) respectively.

Graphing the equations in the xy plane with m an animated parameter is interesting to watch.  One line stays still, one slides up or down, one tilts to meet them on either side.



  Posted by Jer on 2018-01-07 12:29:31
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